Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control

Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control

1st Edition - October 22, 2021

Write a review

  • Editors: Ahmed Radwan, Farooq Khanday, Lobna Said
  • Paperback ISBN: 9780323900898
  • eBook ISBN: 9780323902038

Purchase options

Purchase options
DRM-free (EPub, PDF)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order


Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems.

Key Features

  • Presents a simple and comprehensive understanding of the field of fractional-order systems
  • Offers practical knowledge on the design of fractional-order systems for different applications
  • Exposes users to possible new applications for fractional-order systems


Researchers, graduate students in the fields of basic and applied sciences, electrical engineering, chemical engineering, information security, control theory, solid-state electronics, power engineering, biomedical engineering. Researchers from biological sciences to understand the theories better therein

Table of Contents

  • Cover image
  • Title page
  • Table of Contents
  • Copyright
  • List of contributors
  • Chapter One: Continuous and discrete symmetry methods for fractional differential equations
  • Abstract
  • 1.1. Introduction
  • 1.2. Continuous and discrete symmetry for classical differential equations
  • 1.3. Continuous symmetry for fractional differential equation
  • 1.4. Discrete symmetry for fractional Harry Dym equation
  • 1.5. Conclusion
  • References
  • Chapter Two: Some theoretical and computation results about COVID-19 by using a fractional-order mathematical model
  • Abstract
  • 2.1. Introduction
  • 2.2. Background materials
  • 2.3. Main work
  • 2.4. Series solution of the considered system (2.2) under normal Caputo derivative
  • 2.5. General series solution of the considered system (2.3)
  • Declaration of competing interest
  • References
  • Chapter Three: Spatial-fractional derivatives for fluid flow and transport phenomena
  • Abstract
  • 3.1. Introduction
  • 3.2. Preliminary concepts
  • 3.3. Spatial-fractional mass conservation equation
  • 3.4. Fractional Navier–Stokes equation
  • 3.5. Special cases
  • 3.6. Fractional models of flow in porous media
  • 3.7. Fractional natural gas equation
  • 3.8. Fractional multiphase flows in porous media
  • 3.9. Special cases of two-phase flow
  • 3.10. Fractional convection-diffusion equation
  • 3.11. Conclusion
  • References
  • Chapter Four: On the hybrid fractional chaotic systems: a numerical approach
  • Abstract
  • 4.1. Introduction
  • 4.2. Preliminaries and notations
  • 4.3. Hybrid fractional chaotic models
  • 4.4. Numerical methods for solving hybrid fractional models
  • 4.5. Numerical simulations
  • 4.6. Conclusions
  • Declaration of competing interest
  • References
  • Chapter Five: Iterative processes with fractional derivatives
  • Abstract
  • Acknowledgements
  • 5.1. Introduction
  • 5.2. Preliminary concepts
  • 5.3. Design and analysis of iterative methods using fractional derivatives
  • 5.4. Numerical analysis of the proposed methods
  • 5.5. Concluding remarks
  • References
  • Chapter Six: Design of fractional-order finite-time sliding mode controllers for quadrotor UAVs subjected to disturbances and uncertainties
  • Abstract
  • 6.1. Introduction
  • 6.2. Preliminary results
  • 6.3. Quadrotor system dynamics
  • 6.4. Fractional-order SMC controllers for quadrotors
  • 6.5. Simulation results and discussion
  • 6.6. Conclusion
  • References
  • Chapter Seven: Performance evaluation of fractional character vector control applied for doubly fed induction generator operating in a network-connected wind power system
  • Abstract
  • 7.1. Introduction
  • 7.2. Variable-speed wind power system modeling
  • 7.3. Vector control scheme of DFIG using fractional-order PI controllers
  • 7.4. Design of FOPI controllers applied in the power and current regulation loops
  • 7.5. Numerical results and analysis
  • 7.6. Conclusion
  • References
  • Chapter Eight: Finite time synchronization of discontinuous fractional order Cohen–Grossberg memristive neural networks with discrete delays under sliding mode control strategies
  • Abstract
  • Acknowledgements
  • 8.1. Introduction
  • 8.2. Preliminaries
  • 8.3. Main results
  • 8.4. A numerical example
  • 8.5. Conclusions
  • References
  • Chapter Nine: Variable-order control systems: a steady-state error analysis
  • Abstract
  • 9.1. Introduction
  • 9.2. Variable-order operators
  • 9.3. Main results
  • 9.4. A method for numerical simulation
  • 9.5. Numerical examples
  • 9.6. Conclusion
  • References
  • Chapter Ten: Theoretical study in conformal thermal antennas optimized by a fractional energy
  • Abstract
  • 10.1. Introduction
  • 10.2. Conformal mapping
  • 10.3. Thermal optimization approach
  • 10.4. CTA optimization
  • 10.5. Conformal fractional energy
  • 10.6. Conclusion
  • References
  • Chapter Eleven: Optimal design of fractional-order Butterworth filter with improved accuracy and stability margin
  • Abstract
  • 11.1. Introduction
  • 11.2. Proposed technique
  • 11.3. Simulation results and discussion
  • 11.4. Conclusions
  • References
  • Chapter Twelve: Pseudospectral methods for the Riesz space-fractional Schrödinger equation
  • Abstract
  • 12.1. Introduction
  • 12.2. Space-fractional couplers
  • 12.3. Gegenbauer polynomials and their properties
  • 12.4. Numerical schemes
  • 12.5. Numerical experiments
  • 12.6. Conclusion and discussion
  • References
  • Chapter Thirteen: Transmission line modeling by fractional and topological generalization of the telegrapher's equation
  • Abstract
  • 13.1. Classical and fractional telegrapher's equations
  • 13.2. Reduction of fractional telegrapher's equations to special cases
  • 13.3. Transmission line model
  • 13.4. Transmission line in transient regime
  • 13.5. Transmission line in steady-state regime and its frequency characteristics
  • Appendix 13.A.
  • References
  • Chapter Fourteen: System approach for the frequency analysis of a fractional-order acoustic tube: application for the resonator of the flute instrument
  • Abstract
  • 14.1. Introduction
  • 14.2. Modeling
  • 14.3. Frequency response analysis
  • 14.4. System approach
  • 14.5. Frequency analysis of the system approach
  • 14.6. Conclusions and future work
  • References
  • Chapter Fifteen: Fractional-order dynamics to study neuronal function
  • Abstract
  • 15.1. Introduction
  • 15.2. Fractional calculus definitions
  • 15.3. Fractional-order dynamics in neuroscience
  • 15.4. Discussions and conclusions
  • References
  • Chapter Sixteen: Modeling woody plant tissue using different fractional-order circuits
  • Abstract
  • Acknowledgement
  • 16.1. Introduction
  • 16.2. Woody cell structure
  • 16.3. Bio-impedance models overview
  • 16.4. Experimental setup
  • 16.5. Conclusion
  • References
  • Chapter Seventeen: Analog and digital implementation of fractional-order FitzHugh–Nagumo (FO-FHN) neuron model
  • Abstract
  • 17.1. Introduction
  • 17.2. Fractional-order FitzHugh–Nagumo (FO-FHN) neuron model
  • 17.3. Analog implementations of the FO-FHN neuron model
  • 17.4. FPAA implementation of FO-FHN neuron network
  • 17.5. FPGA implementation of FO-FHN neuron model
  • 17.6. Conclusion
  • References
  • Index

Product details

  • No. of pages: 528
  • Language: English
  • Copyright: © Academic Press 2021
  • Published: October 22, 2021
  • Imprint: Academic Press
  • Paperback ISBN: 9780323900898
  • eBook ISBN: 9780323902038

About the Editors

Ahmed Radwan

Ahmed G. Radwan (Senior member IEEE) is a Professor in the Engineering Mathematics Department, Cairo University, Egypt, and Acting Director of Research, Nile University, Egypt. He was the Former Director of Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. Dr. Radwan was a visiting Professor in Computational Electromagnetic Lab (CEL), Electrical and Computer Engineering department (ECE), McMaster University, Canada in the interval [2008 – 2009], then he was selected to be a part of the first foundation research teams to join KAUST (King Abdullah University of Science and Technology) during the interval [2009 -2011]. His research interests include interdisciplinary concepts between mathematics and engineering applications such as fractional-order systems, bifurcation, chaos, memristor, and encryption. Dr. Radwan received the Cairo University excellence award for research in the engineering sciences in 2016, the Abdul Hameed Shoman Award for Arab Researchers in basic sciences in 2015, the state achievements award for research in mathematical sciences in 2012, the Cairo University achievements award for research in the engineering sciences in 2013, and the best researcher awards Nile University 2015 & 2016. Dr. Radwan has more than 200 papers, h-index 30, and more than 3000 citations based on Scopus database. He is the Co-inventor of Six US patents, author/Co-author of Seven international books as well as 15-chapter books in the highly ranked publishers such as Elsevier and Springer. He received many research grants as Principle Investigator (PI), CO-PI, or Consultant from different national/international organizations. He was Invited to be Lead/Guest Editors in Journal of Circuits, Systems and Signal Processing, and Journal of Mathematical Problems in Engineering, and Complexity. He organized many special sessions, serve as TPC (Technical Program Committee) in several international conferences. He was selected as a member of the first scientific council of Egyptian Young Academy of Sciences (EYAS) as well as in the first scientific council of the Egyptian Center for the Advancement of Science, Technology, and Innovation (ECASTI) to empower and encourage Egyptian young scientists in science and technology and build knowledge-based societies.

Affiliations and Expertise

IEEE Senior Member, Professor, Engineering, Mathematics and Physics Department, Faculty of Engineering, Cairo University; Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

Farooq Khanday

Farooq Ahmad Khanday (M’15, SM’19) received B.Sc., M.Sc., M. Phil. and Ph.D. Degrees from the University of Kashmir in 2001, 2004 2010 and 2013 respectively. From June 2005 to Jan. 2009, he served as Assistant Professor on a contractual basis at the University of Kashmir, Department of Electronics and Instrumentation Technology. In 2009, Dr. Khanday joined the Department of Higher Education J&K and Department of Electronics and Vocational Studies, Islamia College of Science and Commerce Srinagar, as Assistant Professor. In May 2010, he joined as Assistant Professor in the Department of Electronics and Instrumentation Technology, University of Kashmir. His research interests include Fractional-order Circuits, Nano-Electronics, Low-voltage analog integrated circuit design, Hardware Neural Network, Quantum Computing, Stochastic Computing, and Biomedical Circuit Design. Dr. Khanday is the author or co-author of more than 85 publications in peer-reviewed indexed International and National journals/conferences of repute and three book chapters. A book of Dr. Khanday on “Nanoscale Electronic Devices and their Applications” is to appear in July 2020. Dr. Khanday is the Management Committee (MC) Observer of the COST Action CA15225 (Fractional-order systems - analysis, synthesis, and their importance for future design) of the European Union. He is the senior member of IEEE and a member of several professional societies. Dr. Khanday is serving as a reviewer for many reputed International and National scientific journals in Electronics. He has successfully guided many Ph.D., M. Phil scholars, and M. Tech thesis. Dr. Khanday also has completed/ongoing funded research projects to his credit and has established laboratories with state of the art facilities for pursuing research in the field of IC design, Nanoelectronics, fractional-order systems, etc.

Affiliations and Expertise

Srinagar India

Lobna Said

Lobna A. Said is a full-time Assistant Professor at the Faculty of Engineering and Applied Science and the Nano-Electronics Integrated System Research Center (NISC), Nile University (NU). She received the B.Sc. , the M.Sc., and the Ph.D. degrees in electronics and communications from Cairo University, Egypt, in 2007, 2011, and 2016, respectively. She has H-index 15, and more than 660 citations based on the Scopus database. She has over 85 publications distributed between high-impact journals, conferences, and book chapters. She was involved in many research grants as a Senior Researcher, or as a Co-PI from different national organizations. Her research interests are interdisciplinary, including system modeling, control techniques, optimization techniques, analog and digital integrated circuits, fractional-order circuits and systems, non-linear analysis, and chaos theory. She has received the Recognized Reviewer Award from many international journals. She is the Vice-Chair of research activities at the IEEE Computational Intelligence Egypt Chapter. She has received the Excellence Award from the Center for the Development of Higher education and Research in 2016. She is the Winner of Dr. Hazem Ezzat Prize for the outstanding researcher, NU 2019. She is one of the top 10 researchers at NU for the year 2018-2019. Recently, she was selected as a member of the Egyptian Young Academy of Sciences (EYAS) to empower and encourage young Egyptian scientists in science and technology and build knowledge-based societies. In 2020, she was selected to be an affiliate member of the African Academy of Science (AAS). She is in the technical program committee for many International Conferences.

Affiliations and Expertise

Assistant Professor, Faculty of Engineering and Applied Science, Nano-Electronics Integrated System Research Center (NISC), Nile University (NU), Egypt

Ratings and Reviews

Write a review

There are currently no reviews for "Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control"